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4 Feb 2010 16:59:11 IST

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If 7 divides 32^(32^32). what is the reminder?

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If 7 divides 32^(32^32). what is the reminder?

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jatin bansal

Cool goIITian

Joined: 28 Jan 2010

Posts: 31

5 Feb 2010 07:50:15 IST

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32^(32^32)

let(32^32) be y

so32^(32^32)/7 =32^y/7=(32*32*32*------------y times)/7

32^y/7 = [(28+4)*{32*32*-------------------------(y-1) times}]/7

32^y/7 = [28{32*32*----------------------(y-1)times}/7]+[4(32*32*----------------------(y-1)times)}/7

32^y/7 = [4*32^(y-1)]+[4*32^(y-1)]/7

32^y = 7*[4*32^(y-1)] + [4*32^(y-1)]

as you can see that above expression has taken form

dividend = divisor * quotient +remainder

so,remainder = 4*32^(y-1) ,where y=32^32

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